Adaptive Kernel Density Approximation and Its Applications to Real-Time Computer Vision

Density-based modeling of visual features is very common in computer vision research due to the uncertainty of observed data; so accurate and simple density representation is essential to improve the quality of overall systems. Even though various methods, either parametric or non-parametric, are proposed for density modeling, there is a significant trade-off between flexibility and computational complexity. Therefore, a new compact and flexible density representation is necessary, and the dissertation provides a solution to alleviate the problems as follows. First, we describe a compact and flexible representation of probability density functions using a mixture of Gaussians which is called Kernel Density Approximation (KDA). In this framework, the number of Gaussians components as well as the weight, mean, and covariance of each Gaussian component are determined automatically by mean-shift mode-finding procedure and curvature fitting. An original density function estimated by kernel density estimation is simplified into a compact mixture of Gaussians by the proposed method; memory requirements are dramatically reduced while incurring only a small amount of error. In order to adapt to variations of visual features, sequential kernel density approximation is proposed in which a sequential update of the density function is performed in linear time. Second, kernel density approximation is incorporated into a Bayesian filtering framework, and we design a Kernel-based Bayesian Filter (KBF). Particle filters have inherent limitations such as degeneracy or loss of diversity which are mainly caused by sampling from discrete proposal distribution. In kernel-based Bayesian filtering, every relevant probability density function is continuous and the posterior is simplified by kernel density approximation so as to propagate a compact form of the density function from step to step. Since the proposal distribution is continuous in this framework, the problems in conventional particle filters are alleviated. The sequential kernel density approximation technique is naturally applied to background modeling, and target appearance modeling for object tracking. Also, the kernel-based Bayesian filtering framework is applied to object tracking, which shows improved performance with a smaller number of samples. We demonstrate the performance of kernel density approximation and its application through various simulations and experiments with real videos

Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a draft/preprint of one paper submitted to the IEEE Transaction

SMCTC : sequential Monte Carlo in C++

Sequential Monte Carlo methods are a very general class of Monte Carlo methods for sampling from sequences of distributions. Simple examples of these algorithms are used very widely in the tracking and signal processing literature. Recent developments illustrate that these techniques have much more general applicability, and can be applied very effectively to statistical inference problems. Unfortunately, these methods are often perceived as being computationally expensive and difficult to implement. This article seeks to address both of these problems. A C++ template class library for the efficient and convenient implementation of very general Sequential Monte Carlo algorithms is presented. Two example applications are provided: a simple particle filter for illustrative purposes and a state-of-the-art algorithm for rare event estimation

A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain

Detecting camouflaged moving foreground objects has been known to be difficult due to the similarity between the foreground objects and the background. Conventional methods cannot distinguish the foreground from background due to the small differences between them and thus suffer from under-detection of the camouflaged foreground objects. In this paper, we present a fusion framework to address this problem in the wavelet domain. We first show that the small differences in the image domain can be highlighted in certain wavelet bands. Then the likelihood of each wavelet coefficient being foreground is estimated by formulating foreground and background models for each wavelet band. The proposed framework effectively aggregates the likelihoods from different wavelet bands based on the characteristics of the wavelet transform. Experimental results demonstrated that the proposed method significantly outperformed existing methods in detecting camouflaged foreground objects. Specifically, the average F-measure for the proposed algorithm was 0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI

Probabilistic three-dimensional object tracking based on adaptive depth segmentation

Object tracking is one of the fundamental topics of computer vision with diverse applications. The arising challenges in tracking, i.e., cluttered scenes, occlusion, complex motion, and illumination variations have motivated utilization of depth information from 3D sensors. However, current 3D trackers are not applicable to unconstrained environments without a priori knowledge. As an important object detection module in tracking, segmentation subdivides an image into its constituent regions. Nevertheless, the existing range segmentation methods in literature are difficult to implement in real-time due to their slow performance. In this thesis, a 3D object tracking method based on adaptive depth segmentation and particle filtering is presented. In this approach, the segmentation method as the bottom-up process is combined with the particle filter as the top-down process to achieve efficient tracking results under challenging circumstances. The experimental results demonstrate the efficiency, as well as robustness of the tracking algorithm utilizing real-world range information

SMCTC: Sequential Monte Carlo in C++

Sequential Monte Carlo methods are a very general class of Monte Carlo methods for sampling from sequences of distributions. Simple examples of these algorithms are used very widely in the tracking and signal processing literature. Recent developments illustrate that these techniques have much more general applicability, and can be applied very effectively to statistical inference problems. Unfortunately, these methods are often perceived as being computationally expensive and difficult to implement. This article seeks to address both of these problems. A C++ template class library for the efficient and convenient implementation of very general Sequential Monte Carlo algorithms is presented. Two example applications are provided: a simple particle filter for illustrative purposes and a state-of-the-art algorithm for rare event estimation.